Question

@amistre64 Fourth root of 625i, use the following to complete:

Answer 1

http://screensnapr.com/e/HaOnvf.png

Answer 2

5 cos(pi/8)+5 i sin(pi/8)

Answer 3

..How

Answer 4

So how did you get theta?

Answer 5

do you know the position of 625i in the complex plane ?

Answer 6

Nope.

Answer 7

it is on the y axis ( imaginary axis ) so the angle is pi/2

Answer 8

Since its on the imaginary axis?

Answer 9

yep

Answer 10

Alright so that makes sense :D

Answer 11

cool

Answer 12

so for k, is it just n-1? Or what?

Answer 13

@amistre64

Answer 14

for k?

Answer 15

yes

Answer 16

4th root is k=0,1,2,3; so 4 solutions using those values each time

Answer 17

Fourth root of: 0+625i

t = pi/2 (90 degrees)

Answer 18

So if it was 7th root, k=0,1,2,3,4,5,6?

Answer 19

yes

\[\frac{\frac{pi}{2}+2pi(k)}{4}=\frac{\frac{pi+4pi(k)}{2}}{4}=\frac{pi+4pi(k)}{8}\]

Answer 20

Why is it pi+4pi(k)/2? Where did the dividing by two come into play?

Answer 21

common denominator

Answer 22

just simplifying it up by addinging fractions